In the figure, $\triangle ABC$ is an equilateral triangle. Find $m \angle BEC$.
"
Given:
In the figure, $\triangle ABC$ is an equilateral triangle.
To do:
We have to find $m \angle BEC$.
Solution:
$\triangle ABC$ is an equilateral triangle
This implies,
$\angle A = 60^o$
$ABEC$ is a cyclic quadrilateral.
Therefore,
$\angle A + \angle E = 180^o$ (Sum of opposite angles)
$60^o + \angle E = 180^o$
$\angle E = 180^0 - 60^o = 120^o$
Hence $m \angle BEC = 120^o$.
- Related Articles
- In the figure, if $ABC$ is an equilateral triangle. Find $\angle BDC$ and $\angle BEC$."\n
- In the figure, $\triangle PQR$ is an isosceles triangle with $PQ = PR$ and $m \angle PQR = 35^o$. Find $m \angle QSR$ and $m \angle QTR$."\n
- $AD$ is an altitude of an equilateral triangle $ABC$. On $AD$ as base, another equilateral triangle $ADE$ is constructed. Prove that Area($\triangle ADE$):Area($\triangle ABC$)$=3:4$.
- In the figure, $PQRS$ is a square and $SRT$ is an equilateral triangle. Prove that $\angle TQR = 15^o$."\n
- Find the measure of each exterior angle of an equilateral triangle.
- ABC is an equilateral triangle of side $2a$. Find each of its altitudes.
- In \( \triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ} \) and \( \mathrm{BM} \) is an altitude. If \( A M=9 \) and \( C M=16 \), find the perimeter of \( \triangle \mathrm{ABC} \).
- If $\triangle ABC$ and $\triangle BDE$ are equilateral triangles, where $D$ is the mid-point of $BC$, find the ratio of areas of $\triangle ABC$ and $\triangle BDE$.
- In the figure, $PQRS$ is a square and $SRT$ is an equilateral triangle. Prove that $PT = QT$."\n
- Prove that each angle of an equilateral triangle is $60^o$.
- Isosceles Triangle, Equilateral Triangle, Scalene Triangle
- Angles $A, B, C$ of a triangle $ABC$ are equal to each other. Prove that $\triangle ABC$ is equilateral.
- Equilateral Triangle
- In triangle ABC, $\angle A=80^o, \angle B=30^o$. Which side of the triangle is the smallest?
- In figure below, $\triangle ABC$ is right angled at C and $DE \perp AB$. Prove that $\triangle ABC \sim\ \triangle ADE$ and hence find the lengths of \( A E \) and \( D E \)."\n
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies